Many forms of data transmission rely on the modulation of a carrier wave at a transmitter. For example, in quadrature modulation, inphase and quadrature signals (I- and Q-signals) specify symbols from a symbol alphabet. Each transmitted symbol maps to one of the symbols of the symbol alphabet and is defined by a phase and amplitude and is associated with a plurality of bits conveyed by the transmitted signal. When the signal is received, it is necessary to demodulate the signal and to determine which of the symbols of the symbol alphabet the transmitted signal correspond to.
The processing of the signal in a receiver and a transmitter, as well as transmitting the signal, introduce imperfections or distortions into the received signal. When the signal is received an estimation is made as to the information content of the received signal. It is desirable to have a statistical indication of how trustworthy this estimate is. One indicator of this is log-likelihood ratios.
When a signal is received, an estimation of transmitted symbols is made and, in this instance, log-likelihood ratios are applied to this estimation process. Here log-likelihood ratios are an indication of the likelihood that a particular bit of the estimated transmitted symbol is a 0 or a 1 and this is represented as λmk, λmk+1, . . . , λmk+m−1 where m=log2(M) and the symbol alphabet comprises M-symbols (i.e. an M-ary modulation scheme).
The calculation of log-likelihood ratios is computationally intensive and in the past it has been necessary to implement different calculation algorithms for different modulation schemes. Furthermore, known receivers calculate the log-likelihood ratios for each bit of each symbol as it is received, which is computationally intensive. It is therefore desirable to reduce the computational complexity of calculating log-likelihood ratios. It is further desirable to be able to easily calculate log-likelihood ratios for a variety of modulation schemes.